.5x+4=2/3x+1

Solution for .5x+4=2/3x+1 equation:

.5x+4=2/3x+1

We move all terms to the left:

.5x+4-(2/3x+1)=0


Domain of the equation: 3x+1)!=0

x∈R


We get rid of parentheses

.5x-2/3x-1+4=0

We multiply all the terms by the denominator


(.5x)*3x-1*3x+4*3x-2=0

We add all the numbers together, and all the variables

(+.5x)*3x-1*3x+4*3x-2=0

We multiply parentheses

3x^2-1*3x+4*3x-2=0

Wy multiply elements

3x^2-3x+12x-2=0

We add all the numbers together, and all the variables

3x^2+9x-2=0

a = 3; b = 9; c = -2;
Δ = b2-4ac
Δ = 92-4·3·(-2)
Δ = 105
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{105}}{2*3}=\frac{-9-\sqrt{105}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{105}}{2*3}=\frac{-9+\sqrt{105}}{6}
$